The dynamic growth of bacterial cultures: real-time Bayesian estimation of substrate uptake rates in fed-batch fermentations of E. coli

Abstract

Accurate real-time estimation of system states and metabolic parameters is essential for effective bioprocess control. However, the dynamics of microbial adaptation-the rate at which a microorganism adapts to changes in the substrate concentration-is often overlooked, leading to early-stage plant-model mismatches and inaccurate estimation of relevant parameters, such as the biomass yield on carbon source ($Y_{XC}$) or the maximum substrate uptake rate ($q_S^\text{max}$). This work introduces a novel model-based observer for simultaneous state and parameter estimation that explicitly accounts for substrate uptake dynamics. By defining the substrate uptake rate ($q_S(t)$) as a state variable and introducing a random variable (λ) to represent the biomass-specific substrate uptake adaptability rate, we construct a Bayesian estimator that allows proper determination of the states and parameters in fed-batch fermentations of E. coli while maintaining near-zero centered residuals between the plant output and the proposed model stoichiometry. This work advances methods for robust state and adaptive parameter estimation in dynamic bioprocess environments under uncertainty.